The Casimir effect is a quantum phenomenon proposed by Hendrik Casimir in 1948 [1]}. This effect consists of the interaction between two parallel conducting plates placed in the vacuum of a quantum field. This implies modifications in the quantum vacuum and, as a result, the plates are attracted toward each other. The experimental measurement took place ten years after the theoretical prediction [2]}, and the accuracy has increased over the years [3]}, [4]}. In the first study, these ideas were considered for the electromagnetic field. However, any quantum field exhibits this effect. Although the Casimir force for a scalar field in the Gödel universe has been calculated [5]}, in this paper such a study is developed following a different context. Here, the topological structure of the TFD formalism is considered. Then, different topologies, which lead to different compactifications, allow us to obtain the Casimir effect in Gödel space-time at zero and finite temperature.
